Some properties of Wright Operators

This note aims to present novel positive linear operators involving the Wright function. Furthermore, the present research established the moments of these newly defined operators and estimated the convergence rate using the classical modulus of continuity. Additionally, the convergence rate in the Lipschitz spaces, their A-statistical convergence property, and $({\lambda}, {\gamma})$-statistical convergence properties have been covered.Comment: 1

Some Approximation Properties of Modified Jain-Beta Operators

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters α, β, and γ and discuss Voronovskaja asymptotic formula.</jats:p